Tesseract_test

Optical character recognition

  • install Tesseract-OCR for windows https://tesseract-ocr.github.io/
  • add Tesseract-OCR to system environment - path
  • add tessdata to system variables as TESSDATA_PREFIX
  • install pytesseract
In [1]:
# pip install pytesseract
In [2]:
from PIL import Image
import pytesseract as pt
In [3]:
img1 = Image.open("images/image1.png")
img1
Out[3]:
In [4]:
ques1 = pt.image_to_string(img1)
print(ques1)

Problem 2 (10 points) A system composed of n separate components is said to be a parallel
system if it functions when at least one of the components functions. For such a system, if com-
ponent i, which is independent of the other components, functions with probability p;, i = 1,...,n,

what is the probability that the system functions?

Question 1: subscript goes wrong

In [5]:
img2 = Image.open("images/image2.png")
img2
Out[5]:
In [6]:
ques2 = pt.image_to_string(img2, lang = 'eng+grc' )
print(ques2)

Problem 1 (15 points)
Let U be a uniform random variable on (0,1), and suppose that the conditional distribution of

X, given that U = p, is binomial with parameters n and p. Find the probability mass function of

X. [You may need the Beta function B(a, 3) = ie we —a@)8 da = ee

Question 2: Greek letters and mathematics symbols cannot show

In [7]:
img3 = Image.open("images/image3.png")
img3
Out[7]:
In [8]:
ques3 = pt.image_to_string(img3, lang = "equ")
print(ques3)

≓ ∅∠⋆↕∣ ≓↥∃
∂≼⊄⊃∠≖ ⋟∶∫⋤⊐↕⊈∠⊢↕≼↕≓⊈⋟∠∃ ↕∁∅⊈∶ ⊪
In [9]:
img5 = Image.open("images/image5.png")
img5
Out[9]:
In [10]:
ques5 = pt.image_to_string(img5, lang = "eng+equ")
print(ques5)

3. (20 points) (10 + 10) Let Xj,...,X, be ii.d with p.d.f

202* §5 a 2 ae

0 otherwise,

f(z|@) =

where 6 > 0 is the unknown parameter.

(a) What is a one-dimensional sufficient statistic for 0?
In [11]:
img6 = Image.open("images/image6.png")
img6
Out[11]:
In [12]:
ques6 = pt.image_to_string(img6, lang = "eng+equ")
print(ques6)

ca aS

2. {20 points) (10+10) Suppose that Xa.o« kh eee LQ random variables with mean E(X4) =
yu ~ 0 and finite variance a2 > 0. Here p and o2 are the unknown parameters.

ymptotic (nondegenerate) distribution of 1/Xn, where X, = 0 wr a

(a) Find the as
f the first n observations.

the sample mean oO

ag ae an

Question 6: We need a select tool

In [13]:
img7 = Image.open("images/image7.png")
img7
Out[13]:
In [14]:
ques7 = pt.image_to_string(img7, lang = "eng")
print(ques7)





















Question 7: Cannot recognize handwriting.















Other OCR tools




























One hot encoding












In [15]:



    


import numpy as np
import pandas as pd



    













In [16]:



    


# Initial concepts list
Concepts_list = ["quesID",
                 "random variable", 
                 "conditional probability", 
                 "bayes' theorem", 
                 "normal distribution"]



    













In [17]:



    


Questions_concepts_mat = pd.DataFrame(columns = Concepts_list)
Questions_concepts_mat



    















    
Out[17]:











  
    

      
      quesID
      random variable
      conditional probability
      bayes' theorem
      normal distribution
    

  
  
  






















In [18]:



    


# Match question with concepts list
def match(ques, Concepts_list):
    tags = []
    for i in range(len(Concepts_list)):
        if ques.find(Concepts_list[i]) > 0:
            tags.append(Concepts_list[i])
    return(tags)

# Add question to the questions-concepts matrix
def add_question(quesID, ques, Questions_concepts_mat):
    Concepts_list = Questions_concepts_mat.columns[1:]
    tags = match(ques, Concepts_list)
    ques_concepts = np.zeros(len(Concepts_list))
    for i in range(len(tags)):
        ques_concepts = np.where(Concepts_list == tags[i], 1, ques_concepts)
    
    if quesID in np.array(Questions_concepts_mat["quesID"]):
        if (Questions_concepts_mat.loc[Questions_concepts_mat["quesID"] == quesID, 
                                      Questions_concepts_mat.columns != "quesID"] == ques_concepts).values.all():
            print("The question is already included.")
        else:
            Questions_concepts_mat.loc[Questions_concepts_mat["quesID"] == quesID, 
                                      Questions_concepts_mat.columns != "quesID"] = ques_concepts
            print("The question is updated.")
            
    else:
        Questions_concepts_mat.loc[len(Questions_concepts_mat), "quesID"] = quesID
        Questions_concepts_mat.loc[Questions_concepts_mat["quesID"] == quesID, 
                                      Questions_concepts_mat.columns != "quesID"] = ques_concepts
        print("The question is added.")
    
    return(Questions_concepts_mat)



    













In [19]:



    


Questions_concepts_mat = add_question(quesID = "0001",
                                        ques = ques1, 
                                        Questions_concepts_mat = Questions_concepts_mat)
Questions_concepts_mat



    















    






The question is added.










    
Out[19]:











  
    

      
      quesID
      random variable
      conditional probability
      bayes' theorem
      normal distribution
    

  
  
    

      0
      0001
      0
      0
      0
      0
    

  






















In [20]:



    


Questions_concepts_mat = add_question(quesID = "0002",
                                        ques = ques2, 
                                        Questions_concepts_mat = Questions_concepts_mat)
Questions_concepts_mat



    















    






The question is added.










    
Out[20]:











  
    

      
      quesID
      random variable
      conditional probability
      bayes' theorem
      normal distribution
    

  
  
    

      0
      0001
      0
      0
      0
      0
    

    

      1
      0002
      1
      0
      0
      0
    

  






















In [21]:



    


# Add concept function
def add_concept(con, Questions_concepts_mat):
    if con in np.array(Questions_concepts_mat.columns):
        print("The concept is already included.")
    else:      
        Questions_concepts_mat[con] = np.zeros(len(Questions_concepts_mat))
        print("The concept is added.")
    return(Questions_concepts_mat)



    













In [22]:



    


Questions_concepts_mat = add_concept(con = "probability",
                                     Questions_concepts_mat = Questions_concepts_mat)
Questions_concepts_mat



    















    






The concept is added.










    
Out[22]:











  
    

      
      quesID
      random variable
      conditional probability
      bayes' theorem
      normal distribution
      probability
    

  
  
    

      0
      0001
      0
      0
      0
      0
      0.0
    

    

      1
      0002
      1
      0
      0
      0
      0.0
    

  






















In [23]:



    


# Question 1
Questions_concepts_mat = add_question(quesID = "0001",
                                        ques = ques1, 
                                        Questions_concepts_mat = Questions_concepts_mat)
Questions_concepts_mat



    















    






The question is updated.










    
Out[23]:











  
    

      
      quesID
      random variable
      conditional probability
      bayes' theorem
      normal distribution
      probability
    

  
  
    

      0
      0001
      0
      0
      0
      0
      1.0
    

    

      1
      0002
      1
      0
      0
      0
      0.0
    

  






















In [24]:



    


# Question 2
Questions_concepts_mat = add_question(quesID = "0002",
                                        ques = ques2, 
                                        Questions_concepts_mat = Questions_concepts_mat)
Questions_concepts_mat



    















    






The question is updated.










    
Out[24]:











  
    

      
      quesID
      random variable
      conditional probability
      bayes' theorem
      normal distribution
      probability
    

  
  
    

      0
      0001
      0
      0
      0
      0
      1.0
    

    

      1
      0002
      1
      0
      0
      0
      1.0
    

  
























More databases:


    

  • The relationship among concepts
    • 

  • The meaning of each concept
    • 

  • More information for each question
    • 

  • ...
    •